Question

Question #27abc

Answer 1

The vertex is at `(1,-6)`

Explanation:

There are different methods you can use.

A quadratic has the form `ax^2 +bx +c`

`y = x^2 -2x-5` is the equation of a parabola.

The vertex lies on the line of symmetry of the parabola.
It is a vertical line and can be found from `x = (-b)/(2a)`

Once you know the `x`-value, substitute it into the equation of the parabola to find the `y`-value.

`x = (-b)/(2a) = (-(-2))/(2(1)) = 2/2 =1`

Now find `y`

`y = x^2 -2x-5 = (1)^2 -2(1)-5 = -6`

The vertex is at `(1,-6)`

OR:
Completing the square will give the vertex form.

OR:
You can draw the graph by finding points and plotting them and then read the vertex from the points or from the graph.

graph{y=x^2-2x-5 [-9.9, 10.1, -6.56, 3.44]}